Rank-Transformed Dissimilarity Profiles for High-Dimensional Classification

TL;DR

This paper introduces a rank-transformed dissimilarity profiling method that transforms high-dimensional data into class-wise profiles, improving classification performance in low-sample-size scenarios.

Contribution

It proposes a novel dissimilarity-profiling framework with rank transformation that captures distributional differences and enhances robustness for high-dimensional classification.

Findings

Competitive or improved performance on various datasets.

Profiles encode differences in moments and are robust to outliers.

Method is effective when the underlying signal structure is unknown.

Abstract

Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a dissimilarity-profiling classification framework that represents each observation by its class-wise dissimilarity profile, transforming the original feature space into a low-dimensional representation that summarizes how the observation relates to each class. The key idea is to turn a consequence of the curse of dimensionality into signal: high-dimensional geometry can induce systematic within-class and between-class dissimilarity patterns under location, scale, or other distributional changes, and these patterns are captured by the class-wise profiles. Building on this representation, we introduce a rank-transformed algorithm that converts dissimilarities into class-wise rank profiles, yielding a compact representation for classification. The proposed method delivers competitive or improved performance relative to commonly used classifiers on two-class, multi-class, network, and real high-dimensional low-sample-size datasets. To provide insight into the mechanism underlying the method, we analyze a distance-based surrogate and show that the resulting profiles encode differences in first, second, and higher-order moments, while the rank transformation improves robustness to outliers. Together, these results show that rank-transformed dissimilarity profiles provide an adaptive representation for high-dimensional classification when the signal structure is unknown.